My messages to the everything-list:
A short remark. I have decided start with philosophy, as it is more entertaining as mathematical logic. Right now I listen to lectures of Maarten J.F.M. Hoenen (in German)
His title “Controversy in philosophy” took my attention first but he has some more offers. Say now I listen to “What is philosophy”. He speaks a bit too much but I have already got used to him.
The half of his series on controversies has been devoted to realism vs. nominalism. If I understand correctly, your theorem proves that comp implies realism and in my view your argument is a mathematical model for realism. It is interesting to note that Ockam was a nominalist and with his razor he wanted to strip realism away.
By the way, in the middle ages realism was quite popular as it was easier to solve some theological problems this way. At some time, one philosophy department had even two different chairs, one for realism, another for nominalism. Hence Plato’s ideas have not disappeared during Christianity completely.
Prof Hoenen specializes in the middle ages and it gives some charm to his lectures.
Realism and nominalism in philosophy are related to universals (I guess that numbers could be probably considered as universals as well). A simple example:
A is a person;
B is a person.
Does A is equal to B? The answer is no, A and B are after all different persons. Yet then the question would be if something universal and related to a term “person” exists in A and B.
Realism says that universals do exist independent from the mind (so in this sense it has nothing to do with the physical realism and materialism), nominalism that they are just notation and do not exist as such.
It seems that this page is consistent with what Prof Hoenen says
Well, he has not discussed what idealism has to do with universals. Please have a look. If I understand your argument correctly, according to it the universals do exist literally.
I was talking about realism in a sense that universals exist (I am not sure if this could be generalized for all things). My first naive/crazy idea was that this could give some basis to produce qualia related to notation. Neurons somehow distill universals from things and report them.
On the other hand, if we are to write a program that should classify objects, then this program should have some dictionary with categories. That dictionary in some sense should exist. This was my second naive/crazy thought. It would be interesting to look how realism/nominalism is translated into the object-oriented programming.
I like more to take an example with a human being rather than with a name, so let me consider a term “a human being”. So, after all a neural net is some map. It takes some visual, audio, tactile, etc. inputs, processes them and produces some token. What happens then? Presumably it puts this token to the dictionary that produces qualia for the homunculus in the brain (or whomever, this does not matter at this point). Now I would say that if that final qualia corresponded to “a human being” is the same in all brains, than this is realism. If different, then this is nominalism.
Yes, you are right. My interpretation is different from the conventional difference between realism and nominalism. Here one says indeed that each person has something that exists in the objective sense and this something is “a human being”. Well, it we treat qualia ontologically, then I guess, this will be close to realism. Yet one can imagine different scenarios. Under a conventional definition, qualia “human being” is tied with a physical person in the classical sense of the realism. It is necessary however then to explain how a homunculus in the brain retrieves that qualia from a physical person (quantum consciousness?). The scenario that I have described is different in a sense that the communication takes place through physical processes that we know but at the end we may still think of qualia in the ontological sense. Hence one could probably state that this is also the realism (but definitely in some unconventional sense).
The book that Prof Hoenen recommended about realism and nominalism:
Alain de Libera, Der Universalienstreit. Von Platon bis zum Ende des Mittelalters.
Short info on Google Books